Padé-Chebyshev approximants of multivalued analytic functions, variation of equilibrium energy, and the S-property of stationary compact sets

Pade-Chebyshev approximants are considered for multivalued analytic functions that are real-valued on the unit interval . The focus is mainly on non-linear Pade-Chebyshev approximants. For such rational approximations an analogue is found of Stahl's theorem on convergence in capacity of the Pade approximants in the maximal domain of holomorphy of the given function. The rate of convergence is characterized in terms of the stationary compact set for the mixed equilibrium problem of Green-logarithmic potentials. Bibliography: 79 titles.